Determinants - Definition and Notes
What is Determinant?
Determinants are scalar values associated with square matrices that provide information about the properties of the matrices. They are used in mathematics, physics, and engineering. Determinants represent geometric and algebraic properties of matrices and have applications in solving systems of linear equations, finding matrix inverses, and studying linear transformations. They play a fundamental role in linear algebra, helping to analyze vector spaces, eigenvalues, eigenvectors, and transformations. Determinants follow specific rules and formulas for calculation and are essential for understanding matrix operations. They form the basis for advanced mathematical topics and their applications in various scientific and engineering fields.
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Table of Content
1. Definition.
2. Expansion of determinants.
3. Evaluation of determinants.
4. Properties of determinants.
5. Minors and cofactors.
6. Product of two determinants.
7. Summation of determinants.
8. Differentiation and integration of determinants.
9. Application in solving a system of linear equations.
10. Application in co-ordinate geometry. 1
1. Some special determinants.
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